I agree with the others -- you have a stem issue, not handlebar. If you have a threaded stem, it might be a simple matter of just raising it higher. If threadless, you may be able to flip it or you may have to buy a new one with more rise and/or shorter reach. Keep your drop bars for the time being as you might find that you really like them after raising them with a different stem. Drops bars are really nice for riding in windy conditions, but are only effective if you can comfortably ride with them, which usually depends on the height and reach of your stem. Your best bet would be to find a good bike shop to work with you on this, as they might let you try several different stems to find the one that fits you best.

If you don't think you will ever use the drops, even after raising the handlebar, you might want to chop and flop the bar to make bullhorns as others mentioned. I did this on one of my bikes and really like the bullhorns, particularly for city riding. However, bullhorns kind of suck for riding in windy conditions.